86 



NA TURE 



[November 25, 1897 



apparatus would be on the ground or the deck of a ship, and 

 therefore the balloon could be made easily portable. Gold- 

 beaters' skin would be the best material to employ for the 

 covering, and the smallest size of balloon he could recommend 

 for Arctic exploration purposes would be about 7 feet in diameter, 

 with a capacity of 150 cubic feet and able to lift 500 feet of cable. 

 The necessary gas could be stored in steel tubes, or a portable gas- 

 making machine might be carried. The source of electric power 

 would be a dynamo, with which Mr. Bruce supposed every future 

 Arctic expedition would be provided, and this could be operated 

 by wind power, if coal ran short, or even by hand. By giving 

 long and short flashes on the lamps, it would be possible to 

 convey messages in the Morse alphabet. 



Some time ago, G. Jung gave a solution of the problem 

 " to determine by the method of least squares the plane which 

 most nearly coincides with n non-coplanar points." In the 

 Rendiconti del R. Istiiuto Lo/nbardo, ii. xxx. 16, a brief 

 abstract is given of an investigation by the same writer of the 

 reciprocal problem: "Given tt non-concurrent planes, to find 

 the point most nearly determined by them." The correspond- 

 ing problem in plane geometry has been attacked by M. 

 d'Ocagne, and Prof. Jung has thus extended the method to 

 three-dimension space, besides giving a generalisation of certain 

 constructions first investigated by M. Berthot. 



In the Journal of the Royal Statistical Society (September), 

 Mr. W. F. Sheppard considers the calculation of the average 

 square, cube, &c. , of a large number of magnitudes. Supposing 

 that a number of measurements are tabulated to the nearest 

 multiple of a particular unit {e.g. the chest measurements of 

 5732 Scotch soldiers to the nearest inch), the data do not 

 enable us to find exactly the true average measurement or the 

 average square or cube of the magnitudes. Mr. Sheppard 

 shows that the rough value, obtained by supposing each measure- 

 ment to be equal to the nearest multiple of the unit, differs in 

 some cases considerably from the most probable value of the 

 average in question, and he finds that for laws of distribution 

 which satisfy certain conditions a very close approximation to 

 the latter may be obtained by applying certain simple correc- 

 tions to the " i-nugh values " first calculated. 



In the Mathematical Gazette for October we are glad to see 

 that Mr. R. F. Muirhead calls attention to the old treatment of 

 the " Parallelograms of Velocities and Accelerations," which still 

 survives in many otherwise excellent text-books on dynamics. 

 The enunciation often introduces the notion of "a moving point 

 or body possessing simultaneously two velocities," a notion 

 which is meaningless until coexistent velocities (which would 

 better be spoken of as "velocity components") have been 

 defined. The usual (so-called) " proof" tacitly involves the 

 idea of a body moving relatively to a certain base which is itself 

 in motion, but as the word "relative" is generally omitted, 

 and the parallelogram of velocities is usually given before 

 relative motion is considered, and, moreover, is employed in 

 the discussion of relative motion, the learner's mind is often 

 puzzled and he fails to grasp the theorem. Mr. Muirhead 

 rightly contends that the only logical way out of the difficulty is 

 to make relative motion precede the discussion of the 

 parallelogram law, unless, indeed, the latter be regarded merely 

 as a definition of component velocities and acceleration. 



We have received from Mr. R. C. Mossman a copy of a very 

 valuable and laborious investigation of the Meteorology of 

 Edinburgh, based upon observations during the past 132 years, 

 from documents mainly collected by the Scottish Meteorological 

 Society. The work is published in the Transactions of the 

 Royal Society of Edinburgh, and is divided into two parts, the 

 first dealing with the climatic elements for each day of the year, 



NO. 1465, VOL. 57] 



and the second with monthly and annual means, and with 

 secular and other weather changes. The smoothed curves show 

 that the warmest day of the year falls on July 15, and the 

 coldest on January 8. The mean daily maximum temperature 

 is above the annual average (46°'8) from April 26 to October 14, 

 but the mean minimum does not get above the yearly mean until 

 May 12, and it remains above it till October 19. The greatest 

 excess of sun over shade temperature was 76° '8 in March 1892, 

 and the grass minimum thermometer fell I2°"6 below the mini- 

 mum in shade in May 1890. The -mean annual rainfall is 25'86 

 inches ; the wettest period is that embraced in the seven days 

 ending August 18 ; while the period distinguished by the least 

 rain-fall, is the week ending with March 27. One very interesting 

 feature of the discussion is a chronological appendix of remark- 

 able atmospheric phenomena at Edinburgh, extending from 

 1575 to 1895, which has been compiled from a variety of 

 sources. 



A NOTE in Science states that Dr. O. Hoist, of the Geological 

 Survey of Sweden, after two years' leave of absence granted 

 him for the purpose of studying the new gold-fields in Western 

 Australia, has now returned. Dr. Hoist saw the ancient 

 Australian glacial deposit which is supposed to belong to the 

 Permian age, and says there can be no doubt but that it is an 

 indurated boulder-clay. Its age may possibly be somewhat 

 later than heretofore supposed, but not so much later as to 

 detract from the importance of its bearing on the subject of 

 geological climate. In the semi-desert, where Dr. Hoist spent 

 most of his time, the wind did not appear to him to be of any 

 great importance as a geological agent, although dust storms 

 are sometimes reported from the new towns on the border of the 

 desert. One of the Australian geologists has lately made some 

 interesting observations on what resembles a tidal action of the 

 ground water in the sandy region in the interior. The water 

 rises and falls at regular daily intervals, and the oscillations 

 appear to be too great to be explained as resulting from the 

 daily variations in atmospheric pressure. 



The Electrician calls attention to a new development in the 

 design of electrically-propelled pleasure craft, which has been 

 given the name of the "Nymph." Briefly, the "Nymph" is 

 an attachment to an ordinary pleasure boat, sailing ahead of it 

 but rigidly connected to it, the boat containing the accumulator 

 cells and the switch-gear by which is controlled the motor in the 

 body of the swan-shaped tug. The craft is guided or steered by 

 two reins attached to the head of the " swan," and these reins 

 actuate by gear the ordinary rudder. A regulator situated close 

 to the right-hand of the driver enables him to control the speed 

 of the motor and propeller in the " swan," and to go at full or half- 

 speed, ahead or astern. There are sixteen chloride cells of seven- 

 teen plates each, and these, for starting and low speeds, are con- 

 nected to the motor in two parallels of eight cells each, all the cells 

 being used in series for full speed. The total electrical capacity 

 of the battery is about 300 ampere hours, and this is equal to 

 propelling the boat at a speed of eight miles an hour for six 

 hours, or a total distance of about fifty miles, with six people on 

 board. No resistances are used, and neither the field nor the 

 armature is divided up in any way to regulate the speed. The 

 vibration of the boat is perceptibly less than in one containing 

 the motor. Although the arrangement lends itself to graceful 

 design, there is probably considerable loss of efficiency as com- 

 pared with the usual stern propeller. 



The Commission appointed by the German Government to 

 study the plague in Bombay, and which commenced its work 

 under the presidency, of Prof. Dr. GafiT<y last March, has 

 published the results of its labours in several numbers of the 

 Deutsche medicinische Wochenschrift. The report is a very 

 elaborate and exhaustive one, and contains a mass of valuable 



